In this chapter we introduce selected limit theorems on fuzzy quantum space,
namely Egorov’s theorem, Central limit theorem, Weak and strong law of large numbers,
and extreme value theorems for fuzzy quantum space. We also study here the Ergodic
theory for fuzzy quantum space and Ergodic theorems and Poincaré recurrence theorems
for fuzzy quantum dynamical systems, the Hahn-Jordan decomposition and Lebesgue
decomposition for fuzzy quantum space.
Keywords: Egorov’s theorem, Central limit theorem, Weak law of large numbers,
Strong law of large numbers, Fisher-Tippett, Gnedenko theorem, Balkema, de
Haan-Pickands theorem, Birkhoff’s individual ergodic theorem, The representation
theorem, Individual Ergodic Theorem, Poincaré recurrence theorem, Strong
Poincaré recurrence theorem, Hahn-Jordan decomposition, Lebesgue
decomposition.
